兩種快速篩選素數的方法：埃式和歐拉篩法

 兩種篩選素數的方法：埃式和歐拉篩法

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<vector>
#define maxn 1050
using namespace std;
int a[maxn];
bool isprime[1000002];
int num[1000002];
//埃式篩選法 時間複雜度O(nlogn) 
void is_prim(int n){
	n++;
	fill(isprime,isprime+n,1);
	fill(num,num+n,0);
	isprime[1]=0;
	num[1]=0;
	for(int i=2;i<n;i++){
		if(isprime[i]){
			num[i]=num[i-1]+1;
			for(int j=2*i;j<n;j+=i){
				isprime[j]=0;
			}
		}
		else{
			num[i]=num[i-1];
		}
	}
}
//歐拉篩法O(n)
vector<int> Prime(int n){
	bool flag[n+1];//judge whether the number is prime(1 represent a prime,0 represent a non-prime
	fill(flag,flag+n+1,1);
	vector<int> prime;
	int cnt=0;//the total number of primes 
	for(int i=2;i<=n;i++){
		if(flag[i]){
			prime.push_back(i);
			cnt++;
		}
		for(int j=0;j<cnt;j++){//保證每個素數篩掉最小的合數 
			if(i*prime[j]>n) break;
			flag[i*prime[j]]=0;
			if(i%prime[j]==0) break;//exclude the non-prime number which is not minimum 
		}
	}
	return prime; 
}